Advertisements
Advertisements
प्रश्न
Use ruler and compass only for answering this question.
Draw a circle of radius 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P.
Measure and write down the length of any one tangent.
Advertisements
उत्तर
Steps of Construction:
- Draw a circle with centre O and radius 4 cm using a compass.
- Mark a point P on a horizontal line such that OP = 7 cm.
- Join OP.
- Draw the perpendicular bisector of OP to obtain its midpoint, say M.
- With M as centre and radius MO, draw a circle.
- This circle will cut the given circle at two distinct points A and B.
- Join PA and PB.
- PA and PB are the required tangents from the external point P to the given circle.
Measure the length of the tangent.
Length of tangent
`sqrt(OP^2 − "radius"^2)`
= `sqrt(7^2 − 4^2)`
= `sqrt(49 − 16)`
= `sqrt(33)`
= 5.74 cm (approximately)
So, the length of one tangent is 5.74 cm.
APPEARS IN
संबंधित प्रश्न
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle.
Using ruler and compasses only construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and measure its radius.
Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.
Draw two circles of radii 2.5 cm and 3.5 cm respectively so that their centres are 8 cm apart. Draw direct comm on tangents to the circle.
Draw two circles of radii 3 cm and 3.5 cm, their centres being 8 cm apart. Construct a transverse common tangent and measure its length.
Draw two lines AB, AC so that ∠ BAC = 40°:
(i) Construct the locus of the center of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose center lies within the ∠ BAC.
There is a circle with center O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
Draw a circle of radius 2.5 cm. Construct a pair of tangents from a point Pat a distance of 6 cm from the centre of the circle.
